This application proposes new methodology to resolve problems with current instrumental variable (IV) methods (e.g., control function, generalized method of moments, linear IV models) that compare treatments while adjusting for unmeasured confounding with respect to cross-sectional and longitudinal dichotomous, count, and rate outcomes from observational and randomized mental health studies. We focus on the "treated-on-treated" (TOT) treatment effect that has been designated as crucial for health care policy and clinical decisions. The TOT effect is commonly estimated in mental health studies with the "as-treated" effect that has shown to be biased. Current IV methods do not yield unbiased estimates of TOT effects for dichotomous, count, or incidence outcomes in the form of clinically interpretable odds or risk ratios. Because TOT effects involve the receipt of treatments selected by patients and providers, they are vulnerable to selection bias in both observational and randomized trials, for which the TOT effect does not involve comparisons between randomized groups. The innovation of this approach arises from resolving the problems of current IV approaches for the TOT odds and risk ratio based on either cross- sectional or longitudinal outcomes, evaluating IV assumptions under the logistic and log-linear models, and assessing time-varying effect modifiers of treatment as outlined in the Specific Aims: Aim 1: To extend, with assessments of crucial assumptions, non-linear IV structural nested mean (SNM) models for estimating treated-on-treated odds, risk, and incidence ratios to complex observational and randomized contexts, for which such TOT estimates are not obtainable under other IV methods, including the control function and generalized method of moments approaches. Aim 2: To extend the above new methodology in Aim 1 and 2 to longitudinal binary, count, and incidence outcomes in accounting for acute and lagged effects of treatment on outcomes. Aim 3: To extend the longitudinal methodology in Aim 2 to assess time-varying effect modifiers of treatment on longitudinal outcomes. Aim 4: To assess the methods in Aims 1, 2 and 3 with simulations and applications to several randomized and observational studies. Aim 5: To disseminate the resulting methodology with corresponding software, documentation, and web-based tutorials. PUBLIC HEALTH RELEVANCE: The nonlinear instrumental variable structural nested mean model method is extended for estimating treatment on treated odds risk, and incidence ratios for observational and randomized trials with respect to assessing IV assumptions, longitudinal outcomes, and time-varying effect modifiers treatment.